Given that $y = 2e^x (\sin x - \cos x)$, show that \(\frac{\mathrm{d}y}{\mathrm{d}x} = 4

Question

Given that $y = 2e^x (\sin x - \cos x)$, show that $\frac{\mathrm{d}y}{\mathrm{d}x} = 4e^x \sin x$. Hence, find $\displaystyle\displaystyle \displaystyle\int e^x \sin x \, \mathrm{d}x.$

Accepted Answer

$\displaystyle\int\mathrm e^x\sin x\,\mathrm dx=\frac12\mathrm e^x(\sin x-\cos x)+C$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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